feat(data/list/sort): ordered_insert lemmas #1437
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| theorem count_tail : Π (l : list α) (a : α) (h : 0 < l.length), | ||
| l.tail.count a = l.count a - ite (a = list.nth_le l 0 h) 1 0 | ||
| | (_ :: _) a h := by { rw [count_cons], split_ifs; simp } | ||
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Not sure, but maybe this should be l.tail.count a + ite (a = list.nth_le l 0 h) 1 0 = l.count a just to avoid natural number subtraction.
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I thought about this, but it's really intended as a simplification lemma, so I wanted the LHS to be the thing being calculated. If I move the ite to the LHS, at least in my use case, and probably others, the user is just going to have to rearrange the lemma by hand before they can use it.
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Relatedly, I wouldn't mind some nice notation for ite P 1 0.
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The nice notation is if P then 1 else 0. What would be nicer?
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I would be okay with a definition like boole P or similar to mean ite P 1 0. But it doesn't save a lot of space, and I'm not sure how many interesting theorems there are to prove about it.
ChrisHughes24
added
the
ready-to-merge
* feat(data/list/sort): ordered_insert lemmas * add a lemma about L.tail.count
Some straightforward lemmas about the
ordered_insertoperation defined in data/list/sort.lean.